Dominant pole-placement and extra conjugate-pole assignment with the PID controller

This article concentrates on the progression from the recent guaranteed dominant-pole placement method to the additional pole-assignment for any of other poles so that the performance-index of the closed-loop response becomes less or minimum as possible and the response performance remains within the preset requirements. Generally the pole assignment offers an extra pair of conjugate poles at two definite points on the left half-side of the s-plane. One type of the benchmark plants is regulated by the PID controller which its three gains are provided through both these pole placement and assignment methods. The polynomial equation will be proposed to establish its roots as the existence or absence of such a pair of conjugate poles. When compared to another example ignoring the requirements, the closed-loop response will be enhanced if these conjugate poles are recognized. Without a pair of them, the response with performance nearer to the requirements will be preferred.